Comments on Euler’s “De Mirabilibus Proprietatibus Numerorum Pentagonalium”

H. Rademacher

A chapter in Number Theory and Analysis, 1969, pp 257-268 from Springer

Abstract: Abstract In the above mentioned article [1] Euler discusses consequences of his famous identity (1.1) $$ \prod\limits_{m = 1}^\infty {\left( {1 - x^m } \right) = \sum\limits_{n = - \infty }^{ + \infty } {\left( { - 1} \right)^n x^{\omega n} = f\left( x \right)} } $$ where $$ {2}$$ are the so-called pentagonal numbers.

Keywords: Arithmetical Progression; 24th Root; Lacunary Series; Radial Path; Unrestricted Partition (search for similar items in EconPapers)
Date: 1969
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DOI: 10.1007/978-1-4615-4819-5_18

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